Abstract:
Graph Theory has applications in many different fields, especially in combinatorics. In this study, we investigate the methods developed for obtaining error-correcting codes using graphs. First, the codes obtained from cycle and cut-set spaces of a graph are considered. After constructing the codes and giving the decoding schemes, methods for increasing the dimensions of these codes are examined. Then decoding schemes for these new codes are given. Next, a method for obtaining self-dual codes using cubic planar bipartite graphs is examined. The last method covered is to obtain perfect one error-correcting codes using some graphs that are constructed from the Tower of Hanoi Puzzle.
